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A field theory approach to stability of radial equilibria in nonlinear elasticity

Published online by Cambridge University Press:  24 October 2008

J. Sivaloganathan
J. Sivaloganathan
Affiliation:
School of Mathematics, University of Bath, Bath BA2 7AY
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Extract

In this paper we study the stability of a class of singular radial solutions to the equilibrium equations of nonlinear elasticity, in which a hole forms at the centre of a ball of isotropic material held in a state of tension under prescribed boundary displacements. The existence of such cavitating solutions has been shown by Ball[1], Stuart [11] and Sivaloganathan[10]. Our methods involve elements of the field theory of the calculus of variations and provide a new unified interpretation of the phenomenon of cavitation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 589 - 604
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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